最大的细胞布尔函数和完美的灰色代码

Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics Pub Date : 1963-04-01 DOI:10.6028/jres.067b.007

A. J. Goldman, B. Bender

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引用次数: 1

摘要

1 .一个有n个变量的布尔函数，如果它的每一个连接的分量都是Bn的一个面，那么它被认为是t的子集。将最优二进制单错误检测码的Hammin确定推广到具有最大可能元数的所有推进元函数的表征。2分析了一类具有某些特殊性质的Gray码(Bn上的H米尔顿电路)，例如，对于O:Sd:Sn，每条子路径在Bn的d-c1维面上形成2n - d子路径的划分。

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Maximum cellular boolean functions and perfect gray codes

I. A Boolean function of n variables, considered as a subset of t he discl'cLe uni t n-cube Bn> is called cellular if each of its connected components is a face of Bn. Hammin g'~ determination of optimal binary single-error-detectin g codes is generalized to a characteri zation of all propel' cellular functions with the greatest possible number of clements . II. An analysis is made of a class of Gray codes (H amiltonian circuits on Bn) with certain special propcrti es, e.g., ad mi tting for O:Sd:Sn a parti tion in to 2n d subpaths eac h formin g a d-c1 imensional face of Bn.

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Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics

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